一类分数阶微积分的中值定理及应用

Riemann-Liouville分数阶微积分算子是一类带有一个函数的分数阶微积分算子的特殊情形，以Riemann-Liouville分数阶微积分算子的积分中值定理和微分中值定理为基础，我们得到了一类带有一个函数的分数阶微积分算子的积分中值定理和微分中值定理，并给出其在计算方面的一些应用。     

Inversion,chemical complexity,and interstitial transport in spinels

Spinels with the generic chemical formula AB₂O₄ have potential applications in nuclear energy and batteries. In both cases, their functionality is related to mass transport through the crystal. Here, using long-time atomistic simulations, we examine the impact of the cation structure on interstitial transport in two spinel chemistries, inverse MgGa₂O₄ and double MgAlGaO₄. We emphasize two aspects of the transport properties: the unit mechanisms that are described by individual barriers, for which we introduce pole-figure-like plots, and the aggregate behavior of those unit mechanisms. Compared to previous work on normal spinels, we find that inversion significantly reduces the rate of interstitial transport in these structures and has an impact on the stability of defects as they move through the lattice. In particular, B cation interstitials are found to be kinetically stable only in the inverse MgGa₂O₄. These results provide new insight into relationship between structure, chemistry, and transport in spinels.     

Ferroelectric and electromechanical performance of diverse engineered states of Mn-doped 0.75Pb(Mg1/3Nb2/3)O3-0.25PbTiO3 ceramics

The materials processing history has a great influence on their properties and finally determines their application effect. In this paper, the ferroelectric, polarization-switching current, and strain properties of Mn-doped 0.75Pb(Mg_1/3Nb_2/3)O₃-0.25PbTiO₃ ceramics were studied in fresh state, aged state, and poled state, respectively. Compared with the symmetric polarization-electric-field (P-E) hysteresis loops, current-density-electric-field (J-E) curves, and bipolar electric-field-induced strain (S-E) curves in fresh state samples, asymmetric P-E loops, J-E curves, and bipolar S-E curves were obtained in poled state samples. Well-aged-state samples exhibit double hysteresis P-E loop, four peaks J-E curves, and symmetric S-E curves without negative strain. The symmetry-conforming short-range order (SC-SRO) principle of point defects and internal electric field E_i is employed to clarify the different phenomenon of three states. Results indicated that randomly oriented defect polarization P_D in aged samples can reverse the spontaneous polarization P_S back and result in the double hysteresis P-E loop and four peaks J-E curves. The oriented P_D and resulting E_i in poled-state samples will lead to the asymmetric loops and strain memory effect.     

基于秩序与非秩序理论的文创产品卡通形象设计研究

目的 从秩序与非秩序理论出发,研究文创产品卡通形象的设计方法.方法 对秩序与非秩序理论的视觉机制和创制理论进行梳理,结合实例,阐述了其与文创产品卡通形象设计之间的联系,分析文创产品卡通形象中的秩序与非秩序的表现形式,提出基于秩序与非秩序理论文创产品卡通形象设计的主要原则,归纳出一套基于秩序与非秩序理论的文创产品卡通形象设计流程与方法,指导设计实践,并验证这些理论方法在设计实践中有效性与可行性.结论 通过对秩序与非秩序理论的研究,文创产品卡通形象设计时应注意提高辨识度、亲和力和便于衍生设计的原则.探索基于秩序与非秩序理论的设计流程与方法,按照界定主题、主体形象设计、主体形象拓展、衍生品应用四个环节开展整体方案设计,为文创产品卡通形象设计提供新的思路与方法.     

Reduced‐order method for mathematical modeling of multiphase dc‐dc converter

A multiphase dc‐dc converter is effective for miniaturization and achieving high‐power density in a switching power supply. However, its mathematical modeling becomes complex as the phase number of the circuit increases. This study proposes a new modeling method to derive a reduced‐order method in a simple manner. The frequency characteristics of the reduced‐order model are fit to those of the original mathematical model of the multiphase dc‐dc converter. Therefore, the efficacy of the proposed method is validated.     

基于小波变换的分数阶微分算法在肝脏肿瘤CT图像纹理增强中的应用

图像纹理增强过程中容易丢失平滑区域纹理细节，而分数阶微分增强虽然能够非线性保留平滑区域纹理细节，但对频率分辨率敏感。针对这个问题，提出一种基于小波变换的分数阶微分纹理增强算法，应用于平扫计算机断层扫描（CT）图像的肝脏肿瘤区域的纹理增强。首先，通过小波变换将图像感兴趣区分解成多个子带分量；其次，基于分数阶微分定义构造一个带补偿参数的分数阶微分掩膜；最后，使用该掩膜与每个高频子带分量进行卷积并利用小波逆变换重组图像感兴趣区。实验结果表明，该方法在使用较大分数阶次显著增强肿瘤区域的高频轮廓信息的同时，有效地保留了低频平滑的纹理细节：增强后的肝细胞癌区域与原区域相比，信息熵平均增加36.56%，平均梯度平均增加321.56%，平均绝对差值平均为9.287；增强后的肝血管瘤区域与原区域相比，信息熵平均增加48.77%，平均梯度平均增加511.26%，平均绝对差值平均为14.097。     

Numerical analysis of history-dependent hemivariational inequalities and applications to viscoelastic contact problems with normal penetration

In this paper numerical approximation of history-dependent hemivariational inequalities with constraint is considered, and corresponding Céa’s type inequality is derived for error estimate. For a viscoelastic contact problem with normal penetration, an optimal order error estimate is obtained for the linear element method. A numerical experiment for the contact problem is reported which provides numerical evidence of the convergence order predicted by the theoretical analysis.     

Generalised multivariable supertwisting algorithm

The purpose of this paper is to present an extension of the generalised supertwisting algorithm (STA) to the multivariable framework. We begin by introducing an algorithm that may be deemed as a linear, quasicontinuous, or discontinuous multivariable system, depending on the functions that define them. For the class represented by such an algorithm we prove the robust, Lyapunov stability of the origin and characterise the perturbations that preserve its stability. In particular, when its vector field is discontinuous or quasicontinuous our algorithm is endowed with finite‐time stability. Due to its resemblance to the scalar case, we denote such finite‐time stable systems as generalised multivariable STA. Furthermore, the class of finite‐time stable systems comprise the currently available versions of STAs. To finalise, by means of simulation examples, we show that our proposed finite‐time stable algorithms are well suited for signals online differentiation and highlight their dynamical traits.